JNTU B.Tech III Year ANTENNAS AND WAVE PROPAGATION Previous Question Paper (January/February - 2021 - R16)

For a half-wave dipole of length L = λ/2, the current distribution is assumed to be sinusoidal: I(z) = I₀ sin(k(L/2 - |z|)), where k = 2π/λ. The far-field electric field intensity Eθ at a distance r is given by:

The average power radiated P_rad is obtained by integrating the Poynting vector over a closed sphere of radius r:

Substituting the expression for Eθ and integrating from θ = 0 to π and φ = 0 to 2π:

The integral evaluates to the Cosine Integral Ci(x), specifically Ci(2π) ≈ 0.609. The integral result is approximately 1.219. Thus, the radiated power is:

The radiation resistance R_rad is defined by the relation P_rad = (1/2) I₀² R_rad. Equating the two expressions:

Solving for R_rad:

This value represents the radiation resistance of a center-fed half-wave dipole in free space.

A quarter-wave monopole antenna is a vertical radiator with a length equal to one-quarter of the operating wavelength (λ/4), typically mounted over a perfectly conducting ground plane. The ground plane acts as a mirror, creating an image of the monopole that effectively functions as a half-wave dipole. This configuration allows the monopole to exhibit radiation characteristics similar to a half-wave dipole but occupying only half the physical space.

The radiation mechanism is governed by the following key characteristics:

1. Image Theory: The presence of the ground plane induces currents in the ground, which can be represented by an image antenna located below the surface. The combination of the actual monopole and its image forms a virtual half-wave dipole.
2. Radiation Pattern: The radiation pattern in the vertical plane is identical to the upper half of a half-wave dipole. It provides maximum radiation in the horizontal plane (θ = 90°) and zero radiation along the vertical axis (θ = 0°).
3. Input Impedance: Because the monopole acts as half of a dipole, its input impedance is exactly half that of a corresponding half-wave dipole. For a resonant quarter-wave monopole, the input impedance is approximately 36.5 + j0 Ω, assuming a perfectly conducting ground.
4. Directivity and Gain: Since the radiation is restricted to the upper hemisphere, the power is concentrated into half the space of a free-space dipole. Consequently, the directivity of a quarter-wave monopole is twice that of a half-wave dipole, resulting in a gain of approximately 5.15 dBi.

The electric field intensity at a distance r from the monopole is given by:

where η is the intrinsic impedance of free space (120π Ω), I₀ is the peak current at the base, and θ is the angle measured from the vertical axis. In practice, the finite size and conductivity of the ground plane significantly affect the radiation pattern and impedance, often requiring a radial wire system to maintain efficiency.